pythagorean theorem๐๐๐
what does it mean???!! How do we use it??
who named it pythagorean theorem??๐๐
The man on the right is called pythagores, he was the one who discoverd pythagorean theorem so it was named like him.However, he is a greek philosopher and mathematician .His rule is: In a right triangle the square of the length of the hypotenuse is equal to the sum of the squares of the length of other 2 sides. The converse of what he discovered is: if the length of the square of the hypotenuse is equal to the square of the sum of the other 2 sides then this triangle is right.
history!!!!!
More than 4000 years ago,the babyloneans and the chinese already knew that a triangle with the sides 3,4,and 5 must be a right triangle.They used this knowledge to construct right angles. Then a greek scholar named pythagoras was also fascinated by right triangles with these special side rations.He studied them a bit closer and found that the 2 shorter sides of the triangle squared then added together , equal exactly the square of the longest side. And he proved that this doesnt only work for triangles,bur for only right triangles. So, c ^2=a^+b^2
artists (real life sollution)
If the artist needs to draw characters with right faces then he could use the pythagorean theorem to construct his face. ( as in the famous character in the figure.) Example: a^2 + b^2=c^2
cycologists (real life sollution)
To know the distance from the river to any point on the tree of a land a cycologist may use pythagorean theorem to discover this distance. Example: locate point c on any part of the land then a point A on the river and point B on a tree.To know the distance he should add the squares of the length of the other 2 sides.
finding distances (real life sollution)
Example : A house is 12 feet tall. A man is standing 5 feet far from the house. To know the distance from his feet to the top of the house,he can use pythagorean theorem : distance^2=height of the house^2 +distance between the man ans the house^2=144+25=139 .So the distance from his feet to the top of the house=13
pythagorean theorem in real life
To know the measure of each side of a football playground
pythagorean theorem in real life
In T-squares .we have the length of the first side and of the second and 1 right angle ,so we can easily find the length of the third side by pythagorean theorem
right triangles in real life
Right triangled food shape like pizza
right triangles in real life
Sandwiches๐๐๐
right angles in real life
We draw a diogonal of a rectangled television, it will be the hypotenuse of the triangle.so we will have 1 right angle ,hypotenuse and 2 other sides .
right angled triangles in real life
Pyramids
math example
math example in semi equilateral triangle
math example
Notes:๐๐
In a semi equilateral triangle:
1- the angle facing 60 degrees=hypotenusw รradical 3รท2
2- the angle facing 30
degrees=hypotenuseรท2
The Simplest Way To Prove the Pythagorean Theorem